Cooccurrence and constructions

ABSTRACT

A method and system for performing automatic text analysis is described. A local ranking for one or more contexts with respect to a word and a global ranking for one or more contexts are generated. The rankings are based on the frequency with which the contexts appear in a corpus. A statistic may be generated using the local and global rankings, such as a log ratio rank statistic equal to the logarithm of the global rank divided by local rank, to measure the similarity of contexts with respect to words with which they combine. A source matrix of word to context values is then created. Singular value decomposition is used to create sub-matrices from the source matrix. Vectors from the sub-matrices corresponding to context(s) and/or word(s) are then selected to determine term-term or context-context similarity or term-context correspondence.

CLAIM OF PRIORITY

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 60/494,181, filed Aug. 11, 2003, entitled “Cooccurrence andConstructions,” which is incorporated herein by reference in itsentirety.

BACKGROUND

One of the striking developments in computational linguistics in recentyears has been the rapid progress in the automatic analysis of text.This is especially so where the extraction of semantic content isconcerned. The adoption of statistical, corpus-based techniques withinnatural language processing, the continued development of informationextraction techniques, and the emergence of more effective algorithmsfor extracting particular aspects of linguistic and discourse structurehave largely driven such progress. Such algorithms include topic chainsand rhetorical argument structures.

Effective applications have become a reality in a variety of fields,such as machine translation and automatic summarization, due to theprogress of automated text analysis applications. However, currentautomated text analysis applications tend to rely almost solely onlexical cooccurrence, a simple form of linguistic evidence, with verylittle analysis beyond the application of straightforward statisticaltechniques.

For example, the E-Rater™ essay scoring system, described in U.S. Pat.Nos. 6,181,909 and 6,366,759 to Burstein et al., which are incorporatedherein by reference in their entireties, identifies aspects of thecontent, style and rhetorical structure of essays by using contentvectors to induce simple measures of how closely the vocabulary intarget essays matches the vocabulary usage of essays in a training set.The Criterion™ essay feedback system provides feedback regardingpotential grammatical errors to student writers by identifying wordbigrams with low mutual information (i.e., identifying wordcooccurrences with unexpectedly low probability). The C-Rater™ shortanswer scoring system, described in U.S. Patent Publication No.2003/200,077 by Leacock et al., which is incorporated herein byreference in its entirety, automatically scores short-answer questionsby matching answers with an instructor rubric by using word similarityscores derived from corpus cooccurrence frequencies to support detectionof paraphrase. Each of the E-Rater™, Criterion™ and C-Rater™ systems arethe property of the Educational Testing Service.

An instance in which cooccurrence data is used independently oflinguistic structure is Latent Semantic Analysis (LSA), which makes useonly of word cooccurrence within the same document to producecalculations of semantic similarity. LSA similarity scores are generatedby applying singular value decomposition to matrices representing thelog of raw word frequency by document. The resulting matrices can beused to generate cosine similarity scores indicating how similar twowords are in their distribution across documents, or how similar twodocuments are in their choice of vocabulary.

Generally, cooccurrence-based similarity metrics seem to correlate withvarious psycholinguistic measures. However, when cooccurrence-basedmethods, such as LSA, fail, their failures are generally unlike degradedhuman performance (e.g., LSA judgments of semantic similarity can returnhighly valued word pairs where no reviewer can perceive a connection)and the correlations with human judgments are sometimes relatively weak.

While cooccurrence data alone can provide approximately 70 to 90 percentaccuracy in some applications, such as parsing, and in complex appliedtasks, such as essay scoring, improvement beyond such accuracy cannotlikely be achieved without resort to additional linguistic measures.This is so because, for example, the addition or subtraction of a singleword can completely change the interpretation of an entire expression.Accordingly, the limitations of systems depending solely on cooccurrencedata are evident.

Extensive literature addresses systems that use cooccurrence data tomeasure the distributional similarity of words. Such systems typicallycollect cooccurrence statistics, such as bigram and trigram frequencycounts, word by document frequency counts or frequency of word-wordrelationships from a grammatically analyzed corpus. Some systems thenapply an analytical step, such as singular value decomposition, toimprove the quality of the data. A similarity or dissimilarity metric,such as cosine similarity, the Kullback-Leibler divergence or the like,is then applied to yield a ranking which estimates the degree to whichany pair of words have similar or dissimilar distributions.

Such systems have well known limitations and problems. First, theresults are only as good as the corpus used for training. Second, theresults are far more reliable for common words than for words that aremore rare due to a scarcity of data. Finally, these systems ignoreimportant linguistic distinctions such as the difference betweendifferent senses of the same word. Accordingly, the outputs of suchsystems are typically noisy (i.e., words/phrases having low similarityoften appear in result lists).

What are needed are methods and systems for improving the accuracy oftext analysis over methods and systems solely using lexicalcooccurrence.

A need exists for methods and systems of automatically analyzing textusing measurements of lexical structure.

A further need exists for methods and systems for determining thefundamental organizational properties of grammar.

The present invention is directed to solving one or more of theabove-listed problems.

SUMMARY

Before the present methods, systems and materials are described, it isto be understood that this invention is not limited to the particularmethodologies, systems and materials described, as these may vary. It isalso to be understood that the terminology used in the description isfor the purpose of describing the particular versions or embodimentsonly, and is not intended to limit the scope of the invention which willbe limited only by the appended claims.

It must also be noted that as used herein and in the appended claims,the singular forms “a,” “an,” and “the” include plural references unlessthe context clearly dictates otherwise. Thus, for example, reference toa “context” is a reference to one or more contexts and equivalentsthereof known to those skilled in the art, and so forth. Unless definedotherwise, all technical and scientific terms used herein have the samemeanings as commonly understood by one of ordinary skill in the art.Although any methods, materials, and devices similar or equivalent tothose described herein can be used in the practice or testing ofembodiments of the invention, the preferred methods, materials, anddevices are now described. All publications mentioned herein areincorporated by reference. Nothing herein is to be construed as anadmission that the invention is not entitled to antedate such disclosureby virtue of prior invention.

In an embodiment, a method for ranking contexts within which a word in acorpus appears includes, for each word in a corpus, determining a localranking for each of one or more contexts, for each context, determininga global ranking, computing a statistic for each context based on one ormore of the local ranking and the global ranking, and ordering the oneor more contexts based on the computed statistic for each context. Thelocal ranking may include an ordering based on the frequency with whichthe word appears with each context. The global ranking may include anordering based on the overall frequency of each context in the corpus.The computed statistic may include a log rank ratio statistic. The logrank ratio statistic for a context with respect to a word may equal thelogarithm of the global rank for the context divided by the local rankfor the context with the word.

In an embodiment, a method for ranking contexts within which a word in acorpus appears includes, for each word in a corpus, determining a localranking for each of one or more contexts, for each context, determininga global ranking, computing a statistic for each context based on one ormore of the local ranking and the global ranking, and producing a sourcematrix of words by contexts in which an attribute of each context isused as a value for a context-word combination. The local ranking mayinclude an ordering based on the frequency with which the word appearswith each context. The global ranking may include an ordering based onthe overall frequency of each context in the corpus. The computedstatistic may include a log rank ratio statistic. Each value may includea log rank ratio statistic or a frequency for the context in the corpus.

In an embodiment, the method further includes generating a term matrix,a factor-weighting matrix and a content matrix from the source matrix.The method may further include computing term-term similarity based on aterm vector for each term from the term matrix and a weight vector foreach term from the factor-weighting matrix. The method may furtherinclude computing context-context similarity based on a context vectorfor each context from the content matrix and a weight vector for eachcontext from the factor-weighting matrix. The method may further includecomputing term-context correspondence based on a term vector for theterm from the term matrix, a context vector for the context from thecontent matrix, and a weight vector from the factor-weighting matrix.

In an embodiment, a system for ranking contexts within which a word in acorpus appears includes a processor and a processor-readable storagemedium operably connected to the processor. The processor-readablestorage medium contains one or more programming instructions forperforming a method for ranking contexts within which a word in a corpusappears including, for each word in a corpus, determining a localranking for each of one or more contexts, for each context, determininga global ranking, computing a statistic for each context based on thelocal ranking and the global ranking, and ordering the one or morecontexts based on the computed statistic for each context. The localranking may include an ordering based on the frequency with which theword appears with each context. The global ranking may include anordering based on the overall frequency of each context in the corpus.The computed statistic may include a log rank ratio statistic.

In an embodiment, a system for ranking contexts within which a word in acorpus appears includes a processor, and a processor-readable storagemedium operably connected to the processor. The processor-readablestorage medium contains one or more programming instructions forperforming a method for ranking contexts within which a word in a corpusappears including, for each word in a corpus, determining a localranking for each of one or more contexts, for each context, determininga global ranking, computing a statistic for each context based on thelocal ranking and the global ranking, and producing a source matrix ofwords by contexts in which an attribute of each context is used as avalue for a context-word combination. The local ranking may include anordering based on the frequency with which the word appears with eachcontext. The global ranking may include an ordering based on the overallfrequency of each context in the corpus. The computed statistic mayinclude a log rank ratio statistic. Each value may include a log rankratio statistic or a frequency for the context in the corpus.

In an embodiment, the processor-readable storage medium further containsone or more programming instructions for generating a term matrix, afactor-weighting matrix and a content matrix from the source matrix. Theprocessor-readable storage medium may further contain one or moreprogramming instructions for computing term-term similarity based on aterm vector for each term from the term matrix and a weight vector foreach term from the factor-weighting matrix. The processor-readablestorage medium may further contain one or more programming instructionsfor computing context-context similarity based on a context vector foreach context from the content matrix and a weight vector for eachcontext from the factor-weighting matrix. The processor-readable storagemedium may further contain programming instructions for computingterm-context correspondence based on a term vector for the term from theterm matrix, a context vector for the context from the content matrix,and a weight vector from the factor-weighting matrix.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects, features, benefits and advantages of the embodiments of thepresent invention will be apparent with regard to the followingdescription, appended claims and accompanying drawings where:

FIG. 1 depicts an exemplary flow diagram for a method for orderingcontexts according to an embodiment.

FIG. 2 is a block diagram of exemplary internal hardware that may beused to contain or implement the program instructions of a systemembodiment.

DETAILED DESCRIPTION

English grammar is a collection of grammatical constructions, such thateach grammatical English word or phrase is licensed by one or moreconstructions. A linguistic expression is ungrammatical if nocombination of grammatical constructions capable of licensing theexpression exists. In proper English grammar, a construction may definephrases of a particular type by specifying that they can contain aconstituent of a certain kind placed in a certain relationship to aconstituent of another kind to form a particular kind of phrase. Thus,constructions have an internal part, which specifies the kinds ofconstituents that can combine with each other, and an external part,which specifies the kind of constituent that results from thecombination.

With respect to cooccurrence, constructions may be similar to words.Constructions may be assigned meanings, syntactic properties andorganizations, and have semantic contribution and discourse functions.Accordingly, postulating a grammatical construction implies awell-defined set of cooccurrence patterns in linguistic data.

The frequency of a linguistic category may tend to be inverselyproportional to its rank in the frequency distribution (i.e., ƒ=k/r,where k is a constant). Thus, while a small set of words appear oftenenough to provide the bulk of the statistical data, most words mayappear so seldom that it is difficult to obtain reliable statisticalinformation. The basic pattern of this formula may apply more profoundlyto word combinations. In other words, the frequency of word pairs maydrop off more quickly than the frequency of words, and the frequency ofword triplets may drop off even more rapidly.

However, word sequences that correlate with constructions are among themore frequent in the language. For example, sequences such as “him the”or “me this” include only function words, the most frequently usedEnglish words, and have a very high overall frequency. Rarerconstructions may be reliably identified by word sequences which, thoughlow in overall frequency, are quite frequent with some words (e.g.,combinations of a possessive pronoun with the noun “way”).

If the distribution of alternative words occupying the same slot in thesame construction is examined, relatively few words may account for mostinstances of the construction. While a broad range of words arecompatible with a construction, most words seldom appear in theconstruction. Moreover, if a word is distributed among the alternateconstructions with which it is associated, most instances of the wordappear in relatively few constructions despite the word being able toappear in a large set of constructions. Examining the distribution ofconstructions by counting bigrams or trigrams that indicate theconstruction's presence illustrates these points.

A vector space method may be used to calculate, for example,context-context similarities for words in a corpus. The context of aword may include a word sequence or attribute of a word sequence that isassociated with a particular instance of a word in a corpus or document.The context may include a word or words appearing just before or afterthe particular word, other words that modify the particular word, andthe like.

In an embodiment, contexts are instantiated as (a) the immediatelypreceding word; (b) the immediately preceding two word sequence; (c) theword immediately before and the word immediately after in combination;(d) the immediately following word; and (e) the immediately followingtwo word sequence. Other contexts may be used without limitation. Thefollowing data may be collected based on the contexts: (a) the totalfrequency of each word-context combination in the corpus and (b) thetotal frequency with which each context appears with any word in thecorpus.

Contexts may be ranked based on the word with which they are associatedin each instance. In an embodiment, two rankings are applied. The firstranking may be a local ranking, which simply orders the contexts bytheir frequency with each word. In other words, if the context“appearing before barked” appeared so often with the word dog that itwas the most frequent context, it would have local rank one. If“appearing after the” were the next most frequent context with dog, itwould receive local rank two, and so forth. If two or more contexts haveequal local frequencies, the contexts may be assigned a rank equal tothe average of the ranks the contexts would occupy if their frequencieswere distinct.

The second ranking may be a global ranking, which orders the contextswhich actually appear with a word by the overall frequency of thecontexts in the corpus. In other words, if the context “appearing beforebarked” appeared a total of fifty times in the corpus, and “appearingafter the” appeared a total of fifty thousand times in the corpus, thelatter would be assigned a higher global rank than the former. If two ormore contexts have equal global frequencies, the contexts may beassigned a rank equal to the average of the ranks the contexts wouldoccupy if their frequencies were distinct.

FIG. 1 depicts an exemplary flow diagram for a method for orderingcontexts according to an embodiment. As shown in FIG. 1, each contextmay be assigned a local rank 102 and a global rank 104. A statistic,such as a log rank ratio statistic, may then be computed 106 for eachcontext. The log rank ratio statistic may be the logarithm of the globalrank divided by the local rank. The log rank ratio statistic may be usedto identify contexts which are particularly characteristic of a wordsince it evaluates the significance of an entire set of contexts againstone another. In an embodiment, the contexts may be ordered based on thelog rank ratio statistic.

Once all contexts are determined for the words in a corpus, a matrix ofwords by contexts may be produced 108 in which some attribute of thecontexts are used as values. In an embodiment, the value is equal to thefrequency of each context in the corpus. In an alternate embodiment, thevalue is equal to the log rank ratio statistic.

Singular value decomposition (“SVD”) may then be applied to the matrix(or to a sub-matrix reduced to a size small enough to be computationallyfeasible). Any number of factors may be extracted by using singularvalue decomposition. The source matrix may be used to generate 110, forexample, three sub-matrices, such as: (a) a term matrix, (b) afactor-weighting matrix and (c) a content matrix. When the threesub-matrices are multiplied together, the result may approximate thevalues observed in the source matrix, with generalizations induced bythe compression of the information into a smaller number of dimensions.

Given the vectors in the term matrix, similarity of terms to terms maybe induced 112 by the cosine of the angle between vectors in factorspace. Cosine similarity in the term matrix may be the basis forterm-term similarities. In other words, if T stands for the vectorassociated with a term in term space, and S is the factor weight vector,the dot product T·S·S·T may be computed to determine the cosinesimilarity between two terms.

Given the vectors in the context matrix, similarity of contexts tocontexts may be induced 114 similarly to the similarity of terms. If Dstands for the vector associated with a context in context space, and Sis the factor vector weight, the dot product D·S·S·D may be produced todetermine the context-context similarity.

Given a context, terms that fit a context well may be determined 116 bytaking the cosine of the context vector for that context against eachterm vector. This may be used to estimate the class of words that aremost strongly associated with each context. In other words, if T standsfor the term's vector in term space, D stands for the context's vectorin vector space, and S stands for the factor weighting, the dot productT·S·D may be used to compute cosine similarity.

SVD analysis may be performed for training purposes on part of a corpus.For example, the N most frequent words may be used. The SVD may then beextended to the remaining words or contexts in the corpus by exploitingthe interdependence between term and context vectors. In other words,given a vector representing the raw context data for a word notappearing in the original SVD analysis, the product of the vector andthe context matrix may be computed to obtain a term vector for the wordin factor space.

For contexts with equal numbers of elements, the degree to which theyare parallel may be estimated by term-term similarity of the parts. Forexample, if the starting context is mrs. _______, the similarity of thestarting context with another context, such as dr. ______ or john ______may be estimated by computing the cosine between the factor vectors ofmrs. and dr. or john. Similarly, the cosine may be computed for eachsubsequent word in a context.

In an embodiment, inferring potential constructions or grammaticalpatterns may be performed using context data. A list of contexts similarto the original context may be produced. Contexts that do not have aparallel basic structure (i.e., the same number of words with the openposition in the same location) may be removed. The cosine may then becomputed between component words of the original context and the word inthe parallel position in the other context. Contexts where the cosinevalues fall below a threshold may be rejected. Using the resulting listof contexts, the vectors for each word in each list of words that fillthe same position in each context may then be summed. The sum may beused to induce a context vector for that position. As a result, asequence of context vectors that select the appropriate words may becomputed for each position in the construction.

The similarity and/or correspondence data may be used to select anoptimal context, a subset of contexts, an optimal word and/or a subsetof words from the corpus for reasons known to those skilled in the art.In addition, the data may be used to make determinations regardingcontexts within text, such as an essay or a short answer to anassessment examination question, that is analyzed in light of the corpusfor reasons known to those skilled in the art. Such determinations mayinclude verifying grammatical correctness or word choice as part ofevaluating the text.

FIG. 2 is a block diagram of exemplary internal hardware that may beused to contain or implement the program instructions of a systemembodiment. Referring to FIG. 2, a bus 228 serves as the maininformation highway interconnecting the other illustrated components ofthe hardware. CPU 202 is the central processing unit of the system,performing calculations and logic operations required to execute aprogram. Read only memory (ROM) 218 and random access memory (RAM) 220constitute exemplary processor-readable storage devices.

A disk controller 204 interfaces with one or more optional disk drivesto the system bus 228. These disk drives may be external or internalfloppy disk drives such as 210, CD ROM drives 206, or external orinternal hard drives 208. As indicated previously, these various diskdrives and disk controllers are optional devices.

Program instructions may be stored in the ROM 218 and/or the RAM 220.Optionally, program instructions may be stored on a computer readablemedium such as a floppy disk or a digital disk or other recordingmedium, a communications signal or a carrier wave.

An optional display interface 222 may permit information from the bus228 to be displayed on the display 224 in audio, graphic or alphanumericformat. Communication with external devices may optionally occur usingvarious communication ports 226. An exemplary communication port 226 maybe attached to a communications network, such as the Internet or anintranet.

In addition to the standard computer-type components, the hardware mayalso include an interface 212 which allows for receipt of data frominput devices such as a keyboard 214 or other input device 216 such as aremote control, pointer and/or joystick.

An embedded system may optionally be used to perform one, some or all ofthe operations of the present invention. Likewise, a multiprocessorsystem may optionally be used to perform one, some or all of theoperations of the present invention.

While the present invention has been described in conjunction withparticular methods and applications as outlined above, it is evidentthat many alternatives, modifications and variations will be apparent toone of ordinary skill in the art. Accordingly, the particularapplications of this invention as set forth above are intended to beillustrative, not limiting. Modifications or changes may be made withoutdeparting from the spirit or scope of the invention, or may becomeobvious to one skilled in the art after review of the present invention.Such modifications or changes are intended to be included within thescope of this present application.

1-28. (canceled)
 29. A method for generating an automated evaluation ofa corpus by ranking contexts within which a word in said corpus appears,comprising: for each word in said corpus, determining a local rankingfor each of one or more contexts, wherein each context comprises a wordsequence located in a particular arrangement relative to the word,wherein the particular arrangement comprises the relative ordering ofthe word sequence and the word, wherein the local ranking comprises anordering based on the frequency with which each context appears with theword; for each context, determining a global ranking; computing astatistic for each context based on one or more of the local ranking andthe global ranking; ordering the one or more contexts based on thecomputed statistic for each context; and deriving said automatedevaluation from said ordered one or more ordered contexts.
 30. Themethod of claim 29 wherein the global ranking includes an ordering basedon the overall frequency of each context in the corpus.
 31. The methodof claim 29 wherein the computed statistic comprises a log rank ratiostatistic, wherein the log rank ration statistic for a context withrespect to a word may equal the logarithm of the global rank for thecontext divided by the local rank for the context with the word.
 32. Amethod for generating an automated evaluation of a corpus by rankingcontexts within which a word in said corpus appears, comprising: foreach word in a corpus, determining a local ranking for each of one ormore contexts, wherein each context comprises a word sequence located ina particular arrangement relative to the word, wherein the particulararrangement comprises the relative ordering of the word sequence and theword, wherein the local ranking comprises an ordering based on thefrequency with which each context appears with the word; for eachcontext, determining a global ranking; computing a statistic for eachcontext based on one or more of the local ranking and the globalranking; producing a source matrix of words by contexts in which anattribute of each context is used as a value for the context-wordcombination; and deriving said automated evaluation from said sourcematrix of words by contexts.
 33. The method of claim 32 wherein theglobal ranking includes an ordering based on the overall frequency ofeach context in the corpus.
 34. The method of claim 32 wherein thecomputed statistic comprises a log rank ratio statistic, wherein the logrank ratio statistic for a context with respect to a word may equal thelogarithm of the global rank for the context divided by the local rankfor the context with the word.
 35. The method of claim 32 wherein eachvalue comprises a frequency for the context in the corpus.
 36. Themethod of claim 32, further comprising: generating a term matrix, afactor-weighting matrix and a content matrix from the source matrix. 37.The method of claim 36, further comprising: computing term-termsimilarity based on a term vector for each term from the term matrix anda weight vector for each term from the factor-weighting matrix.
 38. Themethod of claim 36, further comprising: computing context-contextsimilarity based on a context vector for each context from the contentmatrix and a weight vector for each context from the factor-weightingmatrix.
 39. The method of claim 36, further comprising: computingterm-context correspondence based on a term vector for the term from theterm matrix, a context vector for the context from the content matrix,and a weight vector from the factor-weighting matrix.
 40. A computerapparatus containing logic instructions that, when performed, produce adocument evaluation by ranking contexts within which a word in a corpusappears, comprising: instructions for obtaining each word in a corpus,and for each such word, determining a local ranking for each of one ormore contexts, wherein each context comprises a word sequence located ina particular arrangement relative to the word, wherein the particulararrangement comprises the relative ordering of the word sequence and theword, wherein the local ranking comprises an ordering based on thefrequency with which each context appears with the word; instructionsfor determining a global ranking for each context; instructions forcomputing a statistic for each context based on one or more of the localranking and the global ranking; instructions for ordering the one ormore contexts based on the computed statistic for each context; andinstructions for returning the ordered one or more contexts for use inautomatically evaluating a written document.
 41. The computer apparatusof claim 40 wherein the global ranking includes an ordering based on theoverall frequency of each context in the corpus.
 42. The computerapparatus of claim 40 wherein the computed statistic comprises a logrank ratio statistic, wherein the log rank ration statistic for acontext with respect to a word may equal the logarithm of the globalrank for the context divided by the local rank for the context with theword.
 43. A computer apparatus containing logic instructions which, whenperformed, produce a document evaluation by ranking contexts withinwhich a word in a corpus appears, comprising: instructions for obtainingeach word in a corpus, and for each said word in said corpus,determining a local ranking for each of one or more contexts, whereineach context comprises a word sequence located in a particulararrangement relative to the word, wherein the particular arrangementcomprises the relative ordering of the word sequence and the word,wherein the local ranking comprises an ordering based on the frequencywith which each context appears with the word; instructions fordetermining a global ranking for each context; instructions forcomputing a statistic for each context based on one or more of the localranking and the global ranking; instructions for producing a sourcematrix of words by contexts in which an attribute of each context isused as a value for the context-word combination; and instructions forreturning the source matrix for use in automatically evaluating awritten document.
 44. The computer apparatus of claim 43 wherein theglobal ranking includes an ordering based on the overall frequency ofeach context in the corpus.
 45. The computer apparatus of claim 43wherein the computed statistic comprises a log rank ratio statistic,wherein the log rank ratio statistic for a context with respect to aword may equal the logarithm of the global rank for the context dividedby the local rank for the context with the word.
 46. The computerapparatus of claim 43 wherein each value comprises a frequency for thecontext in the corpus.
 47. The computer apparatus of claim 43, furthercomprising: instructions for generating a term matrix, afactor-weighting matrix and a content matrix from the source matrix. 48.The computer apparatus of claim 47, further comprising: instructions forcomputing term-term similarity based on a term vector for each term fromthe term matrix and a weight vector for each term from thefactor-weighting matrix.
 49. The computer apparatus of claim 47, furthercomprising: instructions for computing context-context similarity basedon a context vector for each context from the content matrix and aweight vector for each context from the factor-weighting matrix.
 50. Thecomputer apparatus of claim 47, further comprising: instructions forcomputing term-context correspondence based on a term vector for theterm from the term matrix, a context vector for the context from thecontent matrix, and a weight vector from the factor-weighting matrix.